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The existence of invariant measures forC[0,1]-valued diffusions

✍ Scribed by R. v. Vintschger

Publisher: Springer
Year: 1989
Tongue: English
Weight: 316 KB
Volume: 82
Category: Article
ISSN: 1432-2064
DOI: 10.1007/bf00354766

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✦ Synopsis

We prove the existence of an invariant measure for processes arising from a perturbation of the C[0, 1]-valued Ornstein-Uhlenbeck process with a drift taking values in the Cameron-Martin space. We study the infinitesimal generator, and a partial integration on C[0, 1] will yield conditions on the drift which enable us to use arguments of perturbation theory to prove the existence of an invariant measure which is absolutely continuous with respect to the Wiener measure.

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